## Archive for September, 2013

### The Math Humor of *Archer*

*Archer* is an animated comedy series about a spy agency. I shamelessly admit that I am a devoted fan.

The show’s protagonist, Sterling Archer, is a pompous, egocentric misogynist created in the image of James Bond. But don’t expect high-level humor or martinis that are shaken, not stirred. Instead, Archer offers off-color wit and binge drinking, with Sterling delivering such lines as,

Lying is like 95% of what I do.

and

Wait, does Vermont have liquor stores? It has to. It sucks there.

Who can blame you if you find it surprising that I would appreciate such low-brow humor? Especially given the prurient nature of material that I regularly offer on this blog.

Did you hear about the constipated mathematician?

He worked it out with a pencil.What kind of pencil?

A #2 pencil, of course.

But the show also occasionally includes a math reference, like this one.

Who am I, Alan Turing? He was also in

X-Men, remember?

Don’t blame me. I never said that the math references were used correctly.

In Season 2, Episode 5 (“The Double Deuce”), it appears that Archer has difficulty with measurement conversions…

Sterling Archer: “So, how much are we talking here?”

Woodhouse: “Oh, nearly 1,200 pounds.”

Sterling Archer: “What?! Nobody is getting killed over… however much that is in real money.”

But then in Season 4, Episode 12 (“Sea Tunt, Part 1”), he demonstrates an uncanny ability to convert between measurements…

Malory Archer (pointing to a map): The bomb is on the ocean floor here at a depth of 8,000 feet.

Sterling Archer: Or 1,333 fathoms.

Lana Kane: How do you know that?

Sterling Archer: How do you not?

A little later, Sterling remarks that the distance is 0.43 leagues below the surface.

So the show isn’t completely devoid of intellectual content. Just mostly.

Why did the spy hide inside a math book.

Because it was under cover.

I know. Painful. This one any better?

A young woman was having trouble finding a post-doc after getting her doctorate in math, so she applied for a job as a spy. At the interview, she was given a sealed envelope with confidential information. She was told that she shouldn’t open the envelope under any circumstances, and she should deliver it to the fourth floor immediately. She left the interview room and, unable to control herself, she opened the envelope. Inside, a message read, “Well done! You’re the kind of person we’re looking for. Report to the seventh floor.”

### My Son’s New Joke

My son is doing his math homework — he’s in first grade, so it involves writing a certain number, spelling that number, and finding all occurrences of that number in a grid of random numbers called a “Number Hunt.” Based on today’s number, he came up with the following joke:

What number is mostly even but not even?

Eleven.

Not a great joke, to be sure… but as good as most jokes on his dad’s blog, and he’s only six years old.

The homework was frustrating (for me), because my sons are capable of much more.

When my sons ride their bikes through the parking lot, they solve problems involving parking space numbers, the digits on license plates, and other numerical things. They ask me to create “math challenges” for them to think about as they ride. Yesterday, they solved the following three challenges:

- Which license plate has the greatest product if you multiply its four digits together? (The license plate format in Virginia is LLL-DDDD, where L is a letter and D is a digit.)
- How many different license plates are possible with the format LLL-DDDD?
- Each of the three rows in our parking lot has a different number of cars. If our parking lot had a fourth row, how many cars would there be in the fourth row?

For Question 1, Eli realized that the license plate with {9, 7, 6, 5} would have a greater product than the license plate with {9, 7, 6, 3}, since 5 > 3. But then he realized that {9, 9, 8, 2} would be even greater, and he correctly determined that the product is 1,296.

For Question 2, Alex thought it would be 144. His argument was that there would be 6 ways to arrange the letters and 24 ways to arrange the digits, and 6 × 24 = 144. We talked about this, and I pointed out that his answer would be correct if we knew *which* three letters and *which* three digits we were using (and they were all different). He and Eli reconvened and eventually claimed there would be 26^{3} x 10^{4} possible license plates… and being the good father that I am, I let them use the calculator on my phone to find the product.

For Question 3, the number of cars in the three rows was 2, 5, and 8. They extended the pattern and concluded that there would be 11 cars in the non-existent fourth row.

So you can understand why I’d be frustrated that Alex’s homework involved writing the number 11 repeatedly. I thought about telling him not to do it, but then I imagined the following conversation:

Alex: Would you punish me for something I didn’t do?

Teacher: Of course not, Alex.

Alex: Good, because I didn’t do my homework.

Or perhaps he’d just fabricate an excuse:

I thought my homework was abelian, so I figured I could turn it in and then do it.

And finally — should abelian be capitalized?

### Excuses Are Like Graphing Calculators…

You may have noticed that there haven’t been very many new posts on this blog recently. I apologize for that. The following flowchart — an idea blatantly stolen from *Brewster Rocket* — provides my excuse.

Since starting a new job in March, I’ve been working 60-80 hours per week. I’m also serving as the chair of the MathCounts Question Writing Committee. Mix in the time demanded by two energetic, six-year-old boys, and, well, that doesn’t leave a lot of time for making math people laugh on the Internet. Don’t get me wrong — I’ve been funny as hell the past six months, both creating and delivering amazing one-liners. I just haven’t had time to type them up for all of you.

Not that you care about any of that. You come here for jokes, not excuses.

Here’s one about work:

The scientist asks, “Why does it work?”

The engineer asks, “How does it work?”

The project manager asks, “How much will it cost?”

The novelist asks, “Do you want fries with that?”

And here are 11 excuses I could have used, but didn’t:

- I created a great joke but then divided by zero, and the joke burst into flames.
- It’s Isaac Newton’s birthday.
- I could only get arbitrarily close to my computer. I couldn’t actually reach it.
- I had a really funny joke to share, but this blog is too narrow to contain it.
- I was watching the World Series and got tied up trying to prove that it converged.
- I have a solar-powered laptop, and it was cloudy.
- I wrote some jokes in a notebook and locked them in my trunk, but a four-dimensional dog got in and ate it.
- I was typing up some jokes when my wife brought me a doughnut and a cup of coffee. I spent the rest of the night trying to figure out which was which.
- I put some jokes in a Klein bottle, but then I couldn’t find them.
- I was too busy celebrating the coincidence of Einstein’s birthday and Pi Day.
- I was contemplating a formula for Phi Day, determining the first Friday the 13th in 2013, and wondering why Tau Day isn’t more popular than Pi Day.

### Another Bad Email Math Puzzle…

It happened again. I received another email with a number trick that makes the ubiquitous claim, “This will work for everyone!” Sadly, it won’t, but it was kind of cool:

Calculate 39 × (your age) × 259.

The email said, “The result will surprise you.”

It didn’t. I suspected what the value of 39 × 259 would be, so I predicted the result. But if you don’t know the value of that product, then maybe you’ll be surprised.

The trick works well enough if you have a double-digit age. But my friend Ferdinand is 107 years old. His result was 1,080,807, and that just looks like a mess. The results for my six-year-old sons were better, albeit rather unsatisfying.

Ha-rumph. So much for the Internet providing mathematical inspiration.

Here are some similarly uninteresting puzzles that I created:

Calculate 7,373 × (your age) × 137.

Calculate 9,091 × (your age) × 11,111.

Calculate 101 × (your age) × 1,000,100,010,001.

To create more puzzles like this, enter **factor(101010…10101)** into Wolfram Alpha.

For your centenarian friends, try these:

Calculate 101,101 × (your age) × 9,901.

Calculate 3.3 × (your age) × 33.67.

Let’s not forget the little people whose age is still in the single digits:

Calculate 3 × (your age) × 37.

Calculate 41 × (your age) × 271.

And a math joke (or is it?) about age:

I’ve been good with numbers my whole life. When I turned 2, I realized that my age had doubled in one year. This concerned me… at that rate, I’d be 32 in four more years!

And another:

What goes up but never comes down?

Your age.

### Good Luck on Friday the 13th

A friend is taking a business trip today, and I asked if he was worried about flying on Friday the 13th. “I think it’s unlucky to have superstitions,” he replied.

If you’re a baseball player and you see a cross-eyed woman today, you might want to spit in your hat to avoid bad luck. (Or so they say.)

As it turns out, the first Friday the 13th of each year is “Blame Someone Else Day,” so if you don’t like this post, you should defintely let my wife know about it.

To ensure that you point a finger at others on the correct day, wouldn’t it be helpful to know when the first Friday the 13th of the year will occur? Consider yourself lucky, because you’ve stumbled across this post. I have two methods you can use for determining which months contain a Friday the 13th.

**Method 1: Look-Up Table**

Take the last two digits of the year, *yy*.

- Calculate the sum
*yy*+ ⌊*yy*/4⌋. (The notation ⌊*x*⌋ indicates the floor function, which is the greatest integer less than*x*, so ⌊π⌋ = 3 and ⌊7.28⌋ = 7, for example.) - Determine the remainder when that sum is divided by 7.
- Look up the remainder in the table below.

For example, in 2013, the calculations would give 13 + ⌊13/4⌋ = 13 + 3 = 16, which has a remainder of 2 when divided by 7. Since 2013 is a non-leap year, the table tells us that Friday the 13th will occur in September and December this year.

Note that the table only works for dates in the 2000’s. To modify the process for dates in the 1900’s, you need to add 1 in the first step; that is, find the sum *yy* + ⌊*yy*/4⌋ + 1. Then proceed as described above.

Also note that four lines in the table are highlighted in pink and yellow. Leap years always cause problems. The yellow lines in the table indicate years in which an extra Friday the 13th occurs in January or Feburary because of leap year, and the pink lines indicate years in which a Friday the 13th in January or February does not occur because of leap year.

**Method 2: Internet**

Go to http://www.timeanddate.com/calendar, enter the year in question, and examine all 12 months to see which contain a Friday the 13th.

[Ed. Note: Though perhaps more efficient, the use of Method 2 is highly discouraged and less fun than Method 1. Using Method 2 instead of Method 1 will result in the automatic revocation of your Geek Card. Plus, there’s a practical issue: What will you do when you have a time-sensitive need to know the month of the first Friday the 13th in the year 2044, say, and you find yourself in a location without Internet access? *Shudder.* Consequently, learning Method 1 is just as critical to you as learning to calculate change mentally is to a grocery store cashier, who lives in perpetual fear of power outages.]

Incidentally, there is at least one Friday the 13th every year. In addition, every month has four Fridays the 13th in a 28-year period, which means there are an average of 1.71 Fridays the 13th each year. (There is a slight snafu regarding this last fact, because years ending in 00 aren’t leap years if the year is not a multiple of 400, but whatever. It’s true most of the time.)

### Mathematical Discoveries

It’s not everyday that a new mathematical discovery is made. It’s been three years since Perelman proved the Poincaré conjecture, and it was a decade-and-a-half before that when Wiles announced-retracted-resubmitted his proof of Fermat’s Last Theorem. So I was ecstatic when I heard the recent news:

*Nation’s Math Teachers Introduce 27 New Trig Functions*

My favorite new function: *pomen*.

My favorite old functions from the farm: *swine* and *coswine*.

And in case you didn’t make it to the end of that article, I wholeheartedly agree with the last line: “factoring will be cut from the math curriculum entirely because it’s ‘annoying and too fucking hard sometimes.'”

One of my favorite not-in-the-regular-curriculum classroom activities is to tell students that mathematicians have discovered a new integer between 3 and 4. Named after its discoverer, the new integer is called *bleem*, so counting now proceeds as 1, 2, 3, bleem, 4, 5, …

I then give students the following exercises:

- bleem + 2 = ___
- 11 – bleem = ___
- 3 + 7 = ___
- 5 + 8 = ___
- 6 – 1 = ___
- 2 × bleem = ___
- 1 × 6 = ___
- 4 × 8 = ___
- 9 ÷ 2 = ___
- 24 ÷ 4 = ___

It’s much cooler if you tell students that they haven’t yet assigned a symbol to this new integer, and then let the class decide what symbol should be used. You can then use the symbol instead of writing “bleem” in all of the exercises. (The best suggestion made by a student was to use 4 as the symbol for bleem, then use 5 to replace 4, use 6 to replace 5, and so on.)

Good luck with the problems above. And no, an answer key will not be provided.

### You Say It’s Your Birthday…

Well, no, actually it’s not my birthday. And it’s not my friend Jacqui’s birthday, either, but she did just celebrate a milestone with us that she wanted to share. Via email, she announced,

I’ve been alive for two billion seconds, a milestone I passed this morning.

This reminded me of a problem from Steve Leinwand’s book, *Accessible Mathematics*, in which he tells kids his age as a unitless number, then asks them to identify what units he must be using. Along those lines, here are some questions for you.

- How old (in years) is my friend Jacqui?
- What is her date of birth?
- If I tell you that my age is 22,333,444, what units must I be using? Assuming I’m not telling a fib, of course. And what is my age in years and my date of birth?

This reminds me of two math jokes about birthdays.

Statistics show that those who celebrate the most birthdays live longest.

An algebraist remembers that his wife’s birthday is on the (

n– 1)^{st}of the month. Unfortunately, he only remembers this when he is reminded on then^{th}.